Geometry in Architecture

THE MATH AND APPLICATION IN MODERN ARCHITECTURE

BY ALMA ZALO

The preview.• Examples of Architectural designs inspired by

Mathematics

• The motive and/or insight behind some designs.

• Advantages of such designs and the added-value.

• Is it all about the aesthetic value?

Petronas Towers – Kuala, Malaysia Agora Tower – Taipei ,Taiwan

Flatiron building, also Fuller building- NY, USA

The never ending illusion

Ripley’s Building - Ontario

The dancing building – Prague, Czech Republic

The crooked House – Sopot, Poland

The connection with Math.• Designing such enormities is a delicate balancing act. A building not only needs to be

structurally sound and aesthetically pleasing, it also has to comply with planning regulations, bow to budget constraints, optimally fit its purpose and maximize energy efficiency.

• The design process is a complex optimization problem. Advanced digital tools can analyze and integrate the bewildering array of constraints to find optimal solutions.

• Math describes the shapes of the structures to be built, the physical features that have to be understood and, as the language of computers, forms the basis for every step of the modelling process.

Mobius Strip Temple - In China

30 St Mary Axe; nicknamed as The Gherkin, In London, 41 floors, minimize whirlwind around its base, shape maximizes ventilation, uses half the energy others towers the same size use

Incorporating technology • With the help of computers you can model aspects of a building, from its

physics to its appearance. Computer models can simulate things like the way the wind blows around the building or sound waves bounce around inside it.

• Graphic programs can explore different mathematical surfaces and populate them with panels of different textures. The information you get from these models can be pulled together in architectural CAD tool called parametric modelling.

• Parametric models allow you to change a variety of geometrical features while keeping fixed those features you have decided should not change..

• A design team can explore a huge range of design options in a very short period of time;• change geometric features of a building and see how the change affect aerodynamic

properties,

• can explore how complex shapes that are hard to build can be broken down into simpler ones,

• can quickly calculate how much material is needed to estimate the cost.

The results…

The London City Hall on the river Thames. Note the giant helical stair case inside The use of glass and a giant helical staircase in the

interior are supposed to symbolize the transparency and the accessibility of the democratic process.

More on CAD

Surfaces that can be described by mathematical equations — such as slices of cones, tori, or spheres — often form the basis of designs.

This is advantageous when it comes to creating virtual models, as mathematically generated surfaces are easily represented on a computer.

Rather than describing a structure by a large number of individually stored co-ordinates, you only need to store an equation.

The exact shape of the surface can be controlled by varying the parameters in the equation The motive and/or insight behind some designs.

z = e-a(x^2+y^2)

z is the vertical axis in the 3-D coordinate system.The number a determines the shape of the surface.

The first surface has a=1The second surface a=5

The third surface has a=7.

A Mathematically generated surface

World Records;

At over 828 meters (2,716.5 feet) and more than 160 stories, Burj Khalifa holds the following records:

Tallest building in the world

Tallest free-standing structure in the world

Highest number of stories in the world

Highest occupied floor in the world

Highest outdoor observation deck in the world

Elevator with the longest travel distance in the world

Tallest service elevator in the world

The tallest of the super tall…

About that aesthetic value…

Exam question!

What is the name of the tallest building in the world?

The Burj Khalifa.

References

EMAAR. The Tower. n.d. 29 11 2014. <http://www.burjkhalifa.ae/en/TheTower/Design.aspx>.

Freiberger, Marianne. Perfect buildings: the Maths of modern architecture. Ed. Plusadmin. 01 03 2007. 1 12 2014. <http://plus.maths.org/content/perfect-buildings-maths-modern-architecture>.

Nastasi, Alison. 10 Amazing Examples of Architecture Inspired by Mathematics. 20 09 2012. 28 11 2014. <http://flavorwire.com/330293/10-amazing-examples-of-architecture-inspired-by-mathematics/view-all>.